Typically, transition ducts have an aft frame which is attached, or integrated into, the aft end of the duct, facilitating attachment of the duct to the inlet of the turbine first stage. The aft frame is often cooled by means of controlled seal leakage and/or small cooling holes that allow compressor discharge air to pass through the frame. See for example, U.S. Pat. Nos. 6,769,257; 5,414,999; 5,724,816; and 4,652,284. Nevertheless, excessively high temperatures and thermal gradients may be experienced in the vicinity of the transition duct aft end frame. Accordingly, there remains a need for more effective cooling techniques in these areas.